One option the couple visited, according to a source, was a $1.6 million Beverly Hills house that is described as a Cape Cod mini-estate. It has three bedrooms, two bathrooms, a Jacuzzi tub, pool and a kitchen outfitted with state-of-the-art Viking and Sub-Zero appliances.

“They spent a lot of time looking at the house,” an eyewitness tells E! News. “They were clearly interested. It is a perfect place for them because it is walled in.”

Nicole, Joel and baby Harlow—who didn't join her parents yesterday—currently live at Madden’s house in Glendale, which he bought down the street from his brother Joel’s house when he was single.

And with rumors of Richie and Madden getting married later this month, the couple’s recent house hunting is adding fuel to the fire.

In addition, a source tells E! News that Madden’s father, who lives in Maryland, is in town this week to spend more time with his sons and his granddaughter.